Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency. To achieve efficient trade-off designs, an enhanced on-the-fly unsteady adjoint-based aerodynamic and aeroacoustic optimization methodology is developed, which maintains the fidelity of the Navier-Stokes solution for unsteady flow and of the moving-medium Ffowcs Williams-Hawkings (FW-H) formulation for capturing tonal noise. Furthermore, this on-the-fly approach enables a unified architecture for discrete-adjoint sensitivity analysis encompassing both aerodynamics and aeroacoustics, facilitating effective multi-objective weighted optimizations. Subsequently, this proposed methodology is applied to perform trade-off optimizations between aerodynamics and aeroacoustics for a propeller by employing varying weighting factors to comprehend their influence on optimal configurations. The results demonstrate a positive correlation between efficiency and noise sensitivities, and thus indicate an inherent synchronicity where pursing noise reduction through purely aeroacoustic optimization inevitably entails sacrificing aerodynamic efficiency. However, by effectively incorporating appropriate weighting factors (recommended to range from 0.25 to 0.5) into the multi-objective function combined with both aerodynamics and aeroacoustics, it becomes feasible to achieve efficiency enhancement and noise reduction simultaneously. Key findings show that reducing blade planform size and equipping “rotated-S” shaped airfoil profiles in the tip region can effectively restrain noise levels while maintaining aerodynamic performance.